A New Goodness-of-Fit Test: Free Chi-Square (FCS)

Yıl 2021, Cilt: 34 Sayı: 3, 879 - 897, 01.09.2021

Özge Tezel Buğra Kaan Tiryaki Eda Özkul Orhan Kesemen

https://doi.org/10.35378/gujs.743444

Öz

This paper presents a new goodness-of-fit technique for testing the assumption of univariate distributions which is based on the theoretical distribution function of the hypothesized distribution. The existing methods are examined in two different categories: binning and binning-free. The most widely known binning test is the Chi-square test. The Kolmogorov-Smirnov, the Cramer-von Mises and the Anderson-Darling goodness-of-fit tests come to the forefront as the binning-free tests. When tests are evaluated in terms of distributions, it is examined in two different classes: the not distribution-free tests and the distribution-free tests. The desired goodness-of-fit test method for a researcher should be binning-free, distribution-free, more sensitivity, easy to use and fast. In this study, a test method is proposed which provides almost all the options that a researcher would want. The Monte-Carlo simulation methods are used to demonstrate the success of the proposed method. In these simulations, the normality test was applied for symmetric distributions whereas the lognormality test was applied for non-symmetric distributions. The proposed test method has demonstrated superiority in many aspects compared to other selected test methods on both simulations and three different real-life datasets.

Anahtar Kelimeler

Binning free, Distribution free, Goodness-of-fit tests, Test of normality, Monte Carlo simulation

Kaynakça

• Yazici, B., & Yolacan, S., “A comparison of various tests of normality”, Journal of Statistical Computation and Simulation, 77(2):175-183, (2007).
• Romao, X., Delgado, R., Costa, A., “An empirical power comparison of univariate goodness-of-fit tests for normality”, Journal of Statistical Computation and Simulation, 80(5):545-591, (2010).
• Dudewicz, E., & Van Der Meulen, E., “Entropy-based tests of uniformity”, Journal of the American Statistical Association, 76(376):967-974, (1981).
• Crzcgorzewski, P., & Wirczorkowski, R., “Entropy-based goodness-of-fit test for exponentiality”, Communications in Statistics-Theory and Methods, 28(5):1183-1202, (1999).
• Choi, B., & Kim, K., “Testing goodness-of-fit for Laplace distribution based on maximum entropy”, Statistics, 40(6):517-531, (2006).
• Mahdizadeh, M., & Zamanzade, E., “New goodness of fit tests for the Cauchy distribution”, Journal of Applied Statistics, 44(6):1106-1121, (2017).
• Dhumal, B., & Shirke, D., “A modified one-sample test for goodness-of-fit”, Journal of Statistical Computation and Simulation, 85(2):422-429, (2015).
• Gibbons, J., & Chakraborti, S. “Nonparametric statistical inference”. Springer, (2011).
• Bain, L., & Engelhardt, M. “Introduction to probability and mathematical statistics”. Brooks/Cole, (1987).
• Stephens, M., “EDF statistics for goodness of fit and some comparisons”, Journal of the American statistical Association, 69(347):730-737, (1974).
• Cramér, H., “On the composition of elementary errors”, Scandinavian Actuarial Journal, 11(1):13-74, (1928).
• Von Mises, R., “Wahrscheinlichkeitsrechnung und Ihre Anwendung in der Statistik und Theoretischen Physik”, F. Deuticke, 6:13-74, (1931).
• Anderson, T., & Darling, D., “Asymptotic theory of certain goodness of fit criteria based on stochastic processes”, The annals of mathematical statistics, 23(2):193-212, (1952).
• Darling, D., “The kolmogorov-smirnov, cramer-von mises tests”, The Annals of Mathematical Statistics, 28(4):823-838, (1957).
• Stephens, M., “Use of the Kolmogorov-Smirnov, Cramér-Von Mises and related statistics without extensive tables”, Journal of the Royal Statistical Society. Series B (Methodological), 32(1):115-122, (1970).
• Noughabi, H., & Arghami, N., “Monte Carlo comparison of seven normality tests”, Journal of Statistical Computation and Simulation, 81(8):965-972, (2011).
• Farrell, P., & Rogers-Stewart, K., “Comprehensive study of tests for normality and symmetry: extending the Spiegelhalter test”, Journal of Statistical Computation and Simulation, 76(9):803-816, (2006).
• Anderson, T., & Darling, D., “A test of goodness of fit”, Journal of the American statistical association, 49(268): 765-769, (1954).
• Dodge, Y. “The Oxford dictionary of statistical terms”. Oxford University Press on Demand, (2006).
• Jammalamadaka, S. R., & Gupta, A. S. “Topics in Circular Statistics”. London: World Scientific Publishing Co. Pte. Ltd., (2001).
• Ben Sada, A. “Cramer-von Mises test for goodness-of-fit of a single sample”. Retrieved Apr 18, 2018, from MATLAB Central File Exchange, (2015).
• Devore, J. “Probability and Statistics for Engineering and the Sciences”. Cengage Learning, (2015).
• Ramachandran, K., & Tsokos, C. “Mathematical statistics with applications in R”. Elsevier, (2014).
• Onyper, S., Thacher, P., Gilbert, J., Gradess, S., “Class start times, sleep, and academic performance in college: A path analysis”, Chronobiology International, 29(3):318-335, (2012).